% Mizar problem: t7_latwal_1,latwal_1,1066,8 
fof(t7_latwal_1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, B)) ) ) ) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_lattices, axiom,  (! [A] :  (l2_lattices(A) => l1_struct_0(A)) ) ).
fof(cc5_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v3_robbins3(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v8_lattices(A)) ) ) ) ).
fof(reflexivity_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_lattices(A, B, B)) ) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(redefinition_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) ) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(cc1_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) & v2_latwal_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v3_robbins3(A)) ) ) ) ).
fof(cc2_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v5_sheffer1(A) & v1_latwal_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v9_lattices(A)) ) ) ) ).
fof(cc6_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_latwal_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) ) ) ) ).
